Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Move four sticks so there are exactly four triangles.
Can you cut up a square in the way shown and make the pieces into a triangle?
Can you split each of the shapes below in half so that the two parts are exactly the same?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Make a flower design using the same shape made out of different sizes of paper.
Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
Can you make five differently sized squares from the interactive tangram pieces?
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
Exploring and predicting folding, cutting and punching holes and making spirals.
What is the greatest number of squares you can make by overlapping three squares?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?
Reasoning about the number of matches needed to build squares that share their sides.
Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
Can you visualise what shape this piece of paper will make when it is folded?
Make a cube out of straws and have a go at this practical challenge.
Can you make the birds from the egg tangram?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
What shape is made when you fold using this crease pattern? Can you make a ring design?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Follow these instructions to make a three-piece and/or seven-piece tangram.
Follow these instructions to make a five-pointed snowflake from a square of paper.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
Did you know mazes tell stories? Find out more about mazes and make one of your own.
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
These pictures show squares split into halves. Can you find other ways?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
Can you put these shapes in order of size? Start with the smallest.
Ideas for practical ways of representing data such as Venn and Carroll diagrams.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you each work out what shape you have part of on your card? What will the rest of it look like?
In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.